"You thought that collectively you could bring down a member of the Government in penalty for what you thought was a bad policy (on police cuts)."

But the three officers rejected any suggestion that they had plotted together to bring down Mr Mitchell.

The three Police Federation officers in question appear before MPs.

A secret recording made by Mr Mitchell shows that he apologised for swearing at police officers during an incident at the gates of Downing Street but denied using the word "plebs".

However, in comments made after the meeting Mr MacKaill claimed the former Tory chief whip refused to provide an account of the incident.

"My officers got involved in a political campaign which was ill thought-through and has led to a lot of public confidence issues for us," he said.

"I would certainly like to apologise to Mr Mitchell because this added to the already big impact of the Plebgate campaign and it is embarrassing that my force was involved in the way it was."

Andrew Mitchell met the three officers after he was accused of calling officers guarding Downing Street 'plebs'

West Midlands Chief Constable Chris Sims told the committee that he has also written to the former chief whip and would like to meet him in person.

Warwickshire Chief Constable Andy Parker said he was "embarrassed" that his officers had become involved in a heated anti-cuts campaign in the wake of the Plebgate incident.

Chief Constable Andy Parker from Warwickshire Police

The head of Professional Standards, Warwickshire and West Mercia Police told MPs: "My view is that, taken as a whole, the comments made by the federation representatives did have the impact of misleading the public as to what happened in that meeting."

Chief Inspector Jerry Reakes-Williams added: "I think the result was that the public were misled but I do not think it was a deliberate attempt to mislead."

Chief Inspector Jerry Reakes-Williams said he did not think there was "a deliberate attempt to mislead".

The decision not to press ahead with misconduct charges was challenged by the Independent Police Complaints Commission (IPCC), which said there were issues of "honesty and integrity" among the three representatives of the Police Federation.

IPCC Deputy Chair Deborah Glass

Appearing before the MPs, the IPCC's deputy chairwoman Deborah Glass said that she was "absolutely astonished" when a final report came back from the three forces recommending that the officers had no case to answer.

"All I can say is that to me the evidence and the conclusions were so at odds that I needed to put that on the public record."

The Chair of the Home Affairs committee, Keith Vaz, later told the BBC: We hoped very much that this was going to end, the committee is obviously going to produce a report. But there is so much new information here.

"This briefing meeting that took place, with the deputies of all these chief constables, that decided there was no case to answer extraordinarily - after a whole year, at an overall cost of about a quarter of a million pounds, the whole Andrew Mitchell issue - they didn't even take formal minutes at the meeting.

"We found this extraordinary at that level of policing. So there are more letters, I'm afraid, and possibly more witnesses who will have to come and give evidence, he added.